Chemical Adsorption of HF, HCl, and H₂O onto YF₃ and Isostructural HoF₃ Surfaces by First Principles

Abstract

The two elements, yttrium and holmium, form a geochemical twin pair as their cations possess equivalent ratios of charge to radius. However, despite their equal electrostatics, a subtle difference in their fluoride or chloride affinity is known within solutions. In this work, we investigated whether this affinity gap is also present within the solid phase and how it depends on the surface configuration. We modeled adsorptions onto β-YF₃ (waimirite) and isostructural β-HoF₃ by periodic density functional theory. To draw conclusions on the affinity toward fluoride and chloride vs. water, adsorbates of HF, HCl, or H₂O onto any of the four highly abundant surfaces of (010), (100), (011), and (101) were studied. Among others, the conformational landscape was explored by 200 ps of ab initio molecular dynamics. For stoichiometric surfaces of both MF₃, we indeed found stronger adsorptions for HF than HCl. All $\left(hkl\right)·$H₂O showed slightly stronger adsorption energies for HoF₃, while for HF and HCl, the metal preferences varied by the surface. While (100) showed the strongest preference for HoF₃, (101) preferred YF₃ by the same magnitude.

1. Introduction

In nature, the elements yttrium and holmium are trivalent cations of practically identical sizes (107.5 pm for Y(III) vs. 107.2 pm for Ho(III) measured at nine-fold coordination, e.g., as present in waimirite) [1,2]. As most geochemical transport processes are driven by the ratio of charge to radius, both high-field strength elements (HFSE) behave alike and are, therefore, referred to as geochemical twin pairs [3]. However, despite the equal electrostatic behavior, subtle differences between both twin elements have been found in solutions within their affinities toward fluoride or chloride [4,5,6]. It is believed that these small differences are the key forces for the significant decrease in Ho and increase in Y concentrations found in fluoride-rich ores originating from hydrothermal veins [3,4,5,7,8,9,10]. Within these hydrothermal zones, a continuous interplay of dissolving vs. precipitation from the aqueous phase occurs. Modeling this complex system involving a great number of elements in an unknown number of chemical species is a too demanding task to be tackled in its entiretydemanding task that needs to be tackled by quantum chemical methods. However, to begin this long journey of understanding these processes in a step-wise manner, we start with the interfaces of the simple, binary fluorides with the most simple, charge-neutral species of fluoride and chloride, HF and HCl, and contrast them with H₂O. Even this simplistic model contains open-ended questions that need to be answered before moving on to more realistic ones. First, due to the absence of such surface studies, it is unknown how the choice of the surface plane affects the halide affinity, or whether the effect is the same for both twin elements. Second, even the pristine surfaces offer plenty of adsorption structural isomers and conformations leading to a potential energy hypersurface with numerous local minima. We, therefore, scanned these by two methods—ab initio molecular dynamics (AIMD) simulations and a systematic generation of initial molecular arrangements. Moreover, the obtained adsorption energies of well-defined MF₃·Ads structures pose an excellent theoretical foundation for future spectroscopic measurements of any waimirite-structured rare earth element (REE) trifluoride. To the best of our knowledge, not a single computational study of molecular interactions to a yttrium trihalide surface exists for any rare earth element trihalide or waimirite structure type surface.

2. Methodology

2.1. Crystal Structure and Surfaces

The mineral waimirite-Y is constituted of orthorhombic β-YF₃, the low-temperature phase of all middle and late lanthanide trifluorides of SmF₃–LuF₃ [2,11,12]. Its Pnma symmetric unit cell contains four formula units forming distorted tricapped trigonal anti-prisms of nine fluorides around each metal center. Analyzing the stability of the bare surfaces for the prototype structure YF₃ and its geochemical twin compound HoF₃ at quantum chemical conditions, in a previous study we found that 75% (YF₃) or 86% (HoF₃) of the total crystal surface was made from the four low Miller index surfaces of (010), (100), (011), and (101) [13]. For the former three, a stoichiometric, non-polar termination was favored, while (101) preferred a substoichiometric composition, in which each surface unit cell was missing one fluorine atom. For the larger supercells used within the isolated setup shown in Figure 1, this resulted in a nominal surface net charge of $+4$. However, as the applied periodic boundary conditions prohibited a charged surface, each fluorine vacancy instead produced a nominal M(II) center. The most stable and abundant surface of (010) forms a very flat surface of an eight-fold coordinated M(III). The second most abundant surfaces are (011) for YF₃ and (100) for HoF₃ containing M(III) in a six-fold coordination. However, these six-fold polyhedrons possess different shapes and leave M(III) less covered in the case of (100). Both MF₃ agree again on (101) as the third most abundant surface, whose six-fold coordinated M(II) are the most accessible ones within the study.

The bare surfaces are modeled by sufficiently large supercells to avoid artificial adsorbate–adsorbate interactions (see Figure 1). Molecular adsorbates (Ads) of HF, HCl, and H₂O were adsorbed onto these to study the adsorption energy and structure.

2.2. Scan of Conformational Adsorption Space

The vast conformational spaces of possible adsorbate structural isomers and conformations of MF₃·(Ads) were scanned by AIMD and a systematic input generation script. In both, full coverage of the surfaces was probed to directly capture the conformations of multiple adsorbates. Because the atomic structures of YF₃ and HoF₃ surfaces are practically equivalent, we chose to scan the conformational spaces of possible adsorptions using YF₃·(Ads) only. We further limited the conformational space scan to the three major contributing surfaces, as the (100) surface possesses only a minor abundance in YF₃. Onto these surface slabs, a single layer of four HF or H₂O molecules was added. Relaxed slab supercells of the converged thickness of ($2\times 2\times 5$) YF₃-layers for (011) and (101) (see Figure 2a) or ($2\times 1\times 10$) YF₃-layers for (010) were used (see Figure 2b) [13]. For the 1:1 mixed monolayer setup of four HF or HCl with four H₂O molecules onto (010), the surface unit cell was doubled using supercells of ($2\times 2\times 4$) YF₃-layers (see Figure 2c).

Initial temperature tests of up to 873 K onto (010)·(HF) revealed that at higher temperatures some molecules diffuse into the vacuum because their kinetic energies outweigh the rather weak adsorption. Therefore, the AIMD runs were performed at rather cold temperatures of 50–300 K with the majority of simulation time obtained at 200 K (see Table S3). Summing over all respective trajectories, about 60 ps AIMD simulation time was created for the pure monolayer onto each surface of (010), (011), and (101). About 30 ps was produced for the mixed monolayer onto (010). Within the AIMD simulations, adsorption events were judged by distance to the surface atoms (≤260 pm) and visualization. Long-living (≥2 ps) coordination events for each surface and adsorbate were selected as starting conformations for further studies. Moreover, the coordination of short lifetimes (≥350 fs) was also considered if showing structural features not already within the scope.

In a second approach, input structures for atomic structure relaxation were script-generated, varying the adsorbate position perpendicular and in-plane to the surface, as well as rotating the adsorbate. Monolayer structures of YF₃·4HF, YF₃·4H₂O and YF₃·2HF·2H₂O were created for the surfaces of (010), (011), and (101), all as supercells in analogy to Figure 2a,b. For each combination of monolayer and surface 36 start structures were generated From the relaxed 324 structures, the most stable ones were selected for further studies. From both approaches sampling the full monolayer, single adsorbate conformations were extracted and transferred to the isolated adsorption setup of ($4\times 3\times 4$) MF₃-layers for (010) and (100) or ($4\times 4\times 4$) MF₃-layers for (011) and (101) (see Figure 1). All (100)·Ads initial structures originated from transferring adsorbate conformations from the other three surfaces. Each selected YF₃·HF adsorption also posed a starting structure for the respective YF₃·HCl one. The same applied to the YF₃ analogous HoF₃, for which the adsorbate coordinates were transferred from the respective YF₃·(Ads) structures. Overall, an isolated adsorption structural scope of 61 YF₃ and 59 HoF₃ structures were considered. Several of these relaxed into chemically equivalent structures or nearly equivalent conformers of the same structural isomer. Thus, our results are based on a total scope of 44 single adsorbate structural isomers for each MF₃. The respective scopes for each surface and adsorbate are listed in Table S4 and all structural isomers are depicted in Figures S2–S13.

2.3. Computational Details

The same computational setup of Perdew–Burke–Ernzerhof (PBE) functional [14] at a kinetic cutoff of 773 eV was used within the Vienna Ab Initio Simulation Package (VASP) [15,16,17,18] as applied to the surface energies evaluated in [13]. The hard projector augmented wave potentials of H, O, and Cl were applied with valence electron numbers of 6 and 7 for the latter two. The effect of hard vs. normal potential files was tested (see SI Section 1.1 [19,20]). All calculations were performed at the $\Gamma$-point. The surface supercells were built with the python packages pymatgen [21,22] and ASE [23]. A minimum of a 25 Å vacuum was applied to all isolated molecules and perpendicular to the surface plane in all supercells to avoid artificial interaction.

For the first conformational scan approach by AIMD, the NVT ensemble with the Verlet algorithm and the Nosé–Hoover thermostat with a coupling parameter of 1 were applied at a 1 fs time step [24,25,26]. See Table S3 for an overview of the runtimes at temperatures of 50–300 K. To keep the computational time of the AIMD feasible, the monolayer AIMD (setup a and b) were conducted at low precision, applying the RMM-DIIS [27,28] algorithm with preconditioned residuum-minimization (VeryFast) as well as a default self-consistent field (SCF) convergence criteria. The mixed monolayer AIMD (setup c) was conducted with the default (Kosugi) blocked-Davidson algorithm at normal precision with SCF criteria of 10${}^{-5}$ eV.

For the second conformational scan approach of script-generated input structures, the atomic relaxation was conducted via a conjugate gradient algorithm at normal precision with the default convergence criteria.

For the isolated adsorption setup used for the analysis, converged surface supercell sizes were found at ($4\times 3\times 4$) MF₃-layers for (010) and (100) or ($4\times 4\times 4$) MF₃-layers for (101) and (011) (see Figure S1 and Tables S1 and S2). The top two MF₃-layers of each surface (48 atoms for (010) and (100) or 64 atoms for (101) and (011)), as well as the adsorbates were relaxed in atomic coordinates with allowed spin polarization, Gaussian smearing with a width of 0.2 eV, Grimme’s dispersion correction with Becke–Johnson damping (D3(BJ)) [29,30], and accurate precision. SCF criteria of 10${}^{-5}$ eV were applied for geometry optimizations and 10${}^{-6}$ eV for final energies. For difficult SCF cases, symmetry was turned off (ISYM = −1), and/or an additional DFT support grid (.ADDGRID.), and/or a reduced minimal mixing parameter of Kerker’s initial approximation [31] (AMIN) of <0.01 was used. If geometric convergence was neither achieved by the conjugated gradient nor by the RMM-DIIS algorithm [27], the ionic step width (POTIM) was reduced from its default of 0.5 to 0.1 Å. All atomic structure visualizations were conducted in VESTA [32]. Trajectories were visualized in VMD [33].

3. Results

All given results were obtained using the isolated adsorption setup shown in Figure 1. We differentiate two kinds of adsorption energies referred to as bonding energies ($\Delta E_{\mathrm{bond}}$) according to Reaction (1) and interaction energy ($\Delta E_{\mathrm{int}}$) according to Reaction (2). The former is calculated with respect to the relaxed (superscript 0) reactants. Consequently, $\Delta E_{\mathrm{bond}}$ is obtained from the total energy of the relaxed adsorption structure minus the total energy of the relaxed, bare surface supercell and the relaxed isolated adsorbate in vacuum.

$${{\mathrm{MF}}_3}_{\left(\mathrm{surf}\right)}^0+{\mathrm{Ads}}_{\left(\mathrm{gas}\right)}^0\stackrel{\Delta E_{\mathrm{bond}}}{\to }{\mathrm{MF}}_3·{\left(\mathrm{Ads}\right)}_{\left(\mathrm{surf}\right)}^0$$

(1)

$\Delta E_{\mathrm{int}}$ is obtained analogously from non-relaxed reactants, which already possess the same atomic structure as inside the relaxed adsorption product.

$${{\mathrm{MF}}_3}_{\left(\mathrm{surf}\right)}+{\left(\mathrm{Ads}\right)}_{\left(\mathrm{gas}\right)}\stackrel{\Delta E_{\mathrm{int}}}{\to }{\mathrm{MF}}_3·{\left(\mathrm{Ads}\right)}_{\left(\mathrm{surf}\right)}^0$$

(2)

Thus, the difference in both adsorption energies is the atomic structure relaxation of the separated reactants from the relaxed structure of the adsorption product. It is, therefore, labeled as preparation energy ($\Delta E_{\mathrm{prep}}$)

$$\Delta E_{\mathrm{prep}}=\Delta E_{\mathrm{bond}}-\Delta E_{\mathrm{int}}$$

(3)

By the atomic structure relaxation of the adsorbed product, spontaneous dissociations of some adsorbate molecules were observed. These can be classified into two categories. For one, there are the H-bond induced dissociations onto stoichiometric surfaces of several strong HCl adsorptions, whose final hydrogen-to-surface fluorine (H−Fsurf) distance is considerably shorter than the H−Cl one (see Figure S17). In one case, this was followed by a subsequent movement of the Cl atom across the surface leading to a final H−Cl distance of 7 Å (see Figure S6e). However, in all of these H-bond-induced dissociations, the MF₃·Ads stay diamagnetic and no change in the surface metal (M${}_{\mathrm{surf}}$) or partial charges occur.

On the other hand, several adsorptions of HF or HCl onto the electron-rich, substoichiometric (101) surface spontaneously dissociate in a hydride-forming mechanism leading to separately adsorbed halide and hydride (q(H)$=-0.6$ e) anions. By formal oxidation state, two electrons are transferred from the surface to the adsorbate, agreeing with a total change in Bader charges of about 1.4 e. A clear difference is also shown by the spin arrangement. The collinear magnetic moment of 8 ${\mathsf{\mu }}_{\mathrm{B}}$ is found for bare (101) produced by the ferromagnetic arrangement of the eight formal M(II) centers (four each on the top/bottom surfaces), each with an unpaired electron. While this magnetic moment is retained for all non-dissociated (101)·Ads, it reduces to 6 ${\mathsf{\mu }}_{\mathrm{B}}$ within the hydride-forming ones. Within the final structures, these two anions remain either coordinated to the same M${}_{\mathrm{surf}}$ ((101)·H${}_{3\AA }$F/Cl, see Figure S19a), coordinated to two neighboring M${}_{\mathrm{surf}}$, ((101)·H${}_{3.5\AA }$F, see Figure S19b), or with one other M${}_{\mathrm{surf}}$ in-between ((101)·H${}_{7\AA }$F/Cl, see Figure S19c). Due to the charge repulsion, the stability and, thus, the absolute adsorption energy increase by the distance of halide to hydride (see

Table 1. Comparison of the different hydride-forming adsorptions by coordination number (CN${}_{\mathrm{surf}}^{\mathrm{M}}$) and the maximum change in partial charge for one M${}_{\mathrm{surf}}$ ($\Delta q_{\mathrm{surf}}^{\mathrm{M}}$) of the coordination sites(s) vs. the bare (101) charges of $q_{\mathrm{surf}}^{\mathrm{M}\left(\mathrm{II}\right)}=1.7$–1.8 e for six-fold coordinated and $q_{\mathrm{surf}}^{\mathrm{M}\left(\mathrm{III}\right)}=2.2$–2.4 e for seven-fold coordinated M${}_{\mathrm{surf}}$, together with the halide to hydride distances ($R_{\mathrm{X}\cdots \mathrm{H}}$) in pm and adsorption energies in kJ·mol${}^{-1}$.

			HF				HCl
	CN${}_{\mathbf{surf}}^{\mathbf{M}}$	M	${\mathit{R}}_{\mathbf{F}\cdots \mathbf{H}}$	$\mathbf{\Delta }{\mathit{q}}_{\mathbf{surf}}^{\mathbf{M}}$	$\mathbf{\Delta }{\mathit{E}}_{\mathbf{int}}$	$\mathbf{\Delta }{\mathit{E}}_{\mathbf{bond}}$	${\mathit{R}}_{\mathbf{Cl}\cdots \mathbf{H}}$	$\mathbf{\Delta }{\mathit{q}}_{\mathbf{surf}}^{\mathbf{M}}$	$\mathbf{\Delta }{\mathit{E}}_{\mathbf{int}}$	$\mathbf{\Delta }{\mathit{E}}_{\mathbf{bond}}$
(101)·H${}_{3\AA }$F/Cl	6	Y	257	$+0.5$	$-973$	$-315$	285	$+0.4$	$-829$	$-311$
		Ho	262	$+0.5$	$-938$	$-290$	292	$+0.4$	$-807$	$-296$
(101)·H${}_{3.5\AA }$F	6; 7	Y	352	$+0.5$	$-1036$	$-349$	—
		Ho	357	$+0.5$	$-1003$	$-324$
(101)·H${}_{7\AA }$F/Cl	6; 6	Y	681	$+0.5$	$-1081$	$-485$	684	$+0.5$	$-937$	$-482$
		Ho	688	$+0.5$	$-1079$	$-483$	691	$+0.5$	$-937$	$-481$

). (101)·H${}_{3.5\AA }$F was not found to be stable for the respective HCl adsorption. Starting from that structure, the chloride moved across the surface, converging into (101)·H${}_{7\AA }$Cl. On the used $(2\times 2\times 4)$ supercell, this is the maximum distance that the two anions can adopt while being coordinated to the six-fold coordinated M(II) centers. Compared to all other MF₃·Ads, their adsorption energies are much larger and their properties are very different. We, therefore, analyzed them as a separate class of adsorption.

The $\Delta E_{\mathrm{bond}}$ values of Table 1 are plotted separately in Figure 3 to the respective strongest adsorptions of the other MF₃·Ads giving an impression on how large $\Delta E_{\mathrm{bond}}$ is affected by the interplay of the adsorbate type and surface cut, while the metal type only has a minor impact.

The most striking variation in adsorption energies is found along ($hkl$)·HF and ($hkl$)·HCl. The differences between the respective strongest adsorptions onto the same MF₃ ($\Delta \Delta E_{\mathrm{bond}}^{\mathrm{Cl}-\mathrm{F}}$) according to Equation (4) are depicted in Figure 4.

$$\Delta \Delta E_{\mathrm{bond}}^{\mathrm{Cl}-\mathrm{F}}=\Delta E_{\mathrm{bond}}^{\left(hkl\right)·\mathrm{HCl}}-\Delta E_{\mathrm{bond}}^{\left(hkl\right)·\mathrm{HF}}$$

(4)

Both MF₃ bind HF significantly stronger than HCl. The preference for HF over HCl is similar in the three stoichiometric surfaces. Within the F-substoichiometric surface of (101), the preference is considerably smaller. The averages of $\Delta E_{\mathrm{bond}}$ over all surfaces are 8–28 kJ·mol${}^{-1}$ stronger for HF, suggesting that the F−Msurf bond is slightly stronger than the respective chloride one. Consequently, the surface mobility of chloride should be slightly higher. This, together with chloride’s more diffuse electron density resulting in higher spacious demands considering the repulsion with the hydride, indicates why the (101)·H${}_{3.5\AA }$Cl was not found to be stable.

The $\Delta E_{\mathrm{bond}}$ for each non-hydride-forming adsorption is related to $\Delta E_{\mathrm{int}}$ in Figure 5. Naturally, the difference of $\Delta E_{\mathrm{prep}}$ is very low for the weakly adsorbed structures. However, it remains very low for any MF₃·H₂O, while it becomes significant for strong HF adsorptions onto (100) or (011) and even larger than the final $\Delta E_{\mathrm{bond}}$ itself for the respective HCl adsorptions. The latter is caused by the strong H−Cl bond elongation introduced above as H-bond dissociated structures.

In the next step, the effect of the metal type on $\Delta E_{\mathrm{prep}}$ is considered (see Figures S14–S16). While most HoF₃·H₂O adsorb slightly stronger than the respective YF₃·H₂O already prior to relaxation, the preference for HoF₃ very mildly increases further upon relaxation by up to 4 kJ·mol${}^{-1}$. Moreover, all non-hydride-forming MF₃·HF prefer HoF₃ over YF₃ before relaxation by up to 10 kJ·mol${}^{-1}$. However, for most of these, $\Delta E_{\mathrm{prep}}$ hardly affects this preference, with the exception of (011)·HF, for which $\Delta E_{\mathrm{prep}}$ shifts twice that initial preference for HoF₃ to a final preference for YF₃HoF₃ twice to the YF₃ preference. Finally, the non-hydride-forming MF₃·HCl show the strongest preference for HoF₃ of up to 50 or 57 kJ·mol${}^{-1}$ with or without the relaxation of the reactants. However, the effect of $\Delta E_{\mathrm{prep}}$ decreases or increases the preference depending on the adsorption isomer.

In the following, the quantities determining $\Delta E_{\mathrm{bond}}$ are further analyzed. The dependency on the atomic structure parameters of the H-bond angle and distance toward F${}_{\mathrm{surf}}$, as well as the direct coordination of O/F/Cl toward Y/Ho${}_{\mathrm{surf}}$ are visualized in Figure 6. See Table S5 for a comparison of non-/weighted averages over each or all surfaces, as well as Figure S18 for a version of Figure 6, including the hydride-forming adsorptions.

As by the lanthanide contraction, the ionic radii of Y(III) and Ho(III) differ by as little as 0.3 pm [1]; any difference in coordination originates from a different bonding situation. However, we found that the difference in the $\Delta \Delta E_{\mathrm{bond}}^{\mathrm{Y}-\mathrm{Ho}}$ (see Figure S24) is too weak to affect the intra-adsorbate bond lengths, as these stay insensitive to the metal center. By closer contact to the surface, the H-bond angles and distances, as well as the direct coordination distances of O/F/Cl to M${}_{\mathrm{surf}}$ show notable differences between YF₃·Ads and HoF₃·Ads when analyzing each surface separately. On the other hand, the signs of these differences vary by surface. As a result, averaging over all surfaces, the metal-type correlated differences do not persist. Considering all surfaces, only those between the adsorbates survive. These emphasize the considerable distinction between weak H₂O H-bonds vs. strong HF and HCl ones. Moreover, they reveal the high similarity between the latter two, which is also present in the direct coordination when accounting for the gap in ionic radii [1].

Linked to the ionic radii and electronegativities, differences between the adsorbates appear within the partial Bader charges. Due to the high electronegativity of F and, thus, little variance of its strongly negative partial charge, which is already very low ($-0.7$ e) for molecular HF, the adsorption onto MF₃ shows no further reduction (see Figure 7 and Figure S20).

However, for HCl adsorption, the partial charges change significantly compared to molecular HCl due to the low ionic character of the H−Cl bond (see Figure S21). This allows the bonding character of MF₃·HCl to be surface-dependent. For adsorptions towardthat are up to six-fold coordinated M${}_{\mathrm{surf}}$ as present in (100) and (011), the partial charges suggest a strong ionic character comparable to MF₃·HF. This is linked to the formation of the H-bond dissociated Cl⋯H−Fsurf introduced above, for which we find no significant differences between both MF₃ (see Figure S17). Finally, the partial charges of H₂O are only marginally affected by the adsorption (see Figures S22 and S23). Onto all stoichiometric surfaces, the positive charge of H slightly increases by 0.1 e, regardless of CN${}_{\mathrm{surf}}$. Adsorbed at the substoichiometric, electron-rich (101), the positive charge of H is reduced slightly by up to $-0.2$ e. However, in contrast to HF and HCl, no dissociation is observed.

Despite the high similarity between the two MF₃ for the properties discussed above, subtle differences appear within the adsorption energies. The differences between both MF₃ for all adsorptions are weighed with the respective surface abundance ratios (%${}_{\mathrm{surf}}$, Equation (5)) of the ideal crystals taken from [13] and compared in Figure 8.

$$\Delta \Delta E_{\mathrm{bond},\%}^{\mathrm{Y}-\mathrm{Ho}}=\left(\Delta E_{\mathrm{bond}}^{{\mathrm{YF}}_3·\mathrm{Ads}}·{\%}_{\mathrm{surf}}^{{\mathrm{YF}}_3}\right)-\left(\Delta E_{\mathrm{bond}}^{{\mathrm{HoF}}_3·\mathrm{Ads}}·{\%}_{\mathrm{surf}}^{{\mathrm{HoF}}_3}\right)$$

(5)

Note that HoF₃ possesses higher %${}_{\mathrm{surf}}$ than YF₃ for the surfaces of (010) and (100) but lower ones for (011) and (101). See Figure S24 for the corresponding non-weighted differences ($\Delta \Delta E_{\mathrm{bond}}^{\mathrm{Y}-\mathrm{Ho}}$) together with the respective %${}_{\mathrm{surf}}$.

Even though the non-weighted H₂O adsorptions bind slightly stronger to HoF₃ than YF₃ regardless of the surface cut, the different %${}_{\mathrm{surf}}$ of the two MF₃ impose a surface dependency for $\Delta \Delta E_{\mathrm{bond},\%}^{\mathrm{Y}-\mathrm{Ho}}$. In contrast, the binding preference for HoF₃ or YF₃ shown by HF or HCl varies inherently between the different surfaces. At the eight-fold coordinated M${}_{\mathrm{surf}}$ of (010), HF and HCl, both slightly prefer HoF₃. While the $\Delta \Delta E_{\mathrm{bond},\%}^{\mathrm{Y}-\mathrm{Ho}}$ of HF is about the same as H₂O, it is lowest for HCl. By the better accessible M${}_{\mathrm{surf}}$ of (100), the %${}_{\mathrm{surf}}$-weighted preferences for HoF₃ grow considerably, yielding the strongest for (100)·HF within all ($hkl$)·Ads. In contrast, all $\Delta \Delta E_{\mathrm{bond},\%}^{\mathrm{Y}-\mathrm{Ho}}$ at (011) prefer YF₃ due to the flipped order in surface abundances. Although (011) also contains six-fold coordinated M${}_{\mathrm{surf}}$, these are less accessible (see Figure 1). In agreement with the metal accessibility, the magnitude of $\Delta \Delta E_{\mathrm{bond},\%}^{\mathrm{Y}-\mathrm{Ho}}$ is only marginally larger than in (010). Finally, for the hydride-forming adsorptions of (101), the higher %${}_{\mathrm{surf}}$ of YF₃ amplifies the inherent preference for the lighter twin element. We believe that this difference primarily originates from the ionization potentials (IP) of M(II), which are measured to be 20.5 eV for Y(II) and 22.8 eV for Ho(II) in the gas phase [35,36]. It may be assumed that the qualitative relation of considerably easier Y(II) than Ho(II) oxidation remains the same for six-fold coordinated metal centers. It should be noted that Ho(II) is measured to have a 4f${}^{11}$ configuration [36], which is not possible with the applied 4f${}^{10}$-in-core potential developed for the stable oxidation state of Ho(III). Therefore, no quantitative relation of $\Delta$IP to $\Delta \Delta E_{\mathrm{bond}}^{\mathrm{Y}-\mathrm{Ho}}$ may be drawn.

Comparing our quantum chemical results with experiments and theoretical studies in solutions at elevated temperatures, we find an agreement of the preference for fluoride over chloride found for Y(III) in aqueous solutions by AIMD simulations [6]. This suggests that the preference is present in different phases of Y(III). A solubility study in aqueous HF compared the fluoride affinity of Y(III) vs. Ho(III) [4]. At high HF concentrations, they found a higher fluoride affinity by Y(III). In another study applying AIMD and in situ X-ray experiments onto aqueous NaCl solutions, the chloride affinity of Y(III) was also found to be higher compared to Ho(III) [5]. Within our study, however, the marginal difference in fluoride or chloride affinity shown between the two metals is much lower than between the surfaces. This demonstrates that, compared to the free ions in solution, the difference in binding affinity at the surface is very sensitive to the surface geometry and termination, even when the respective ions are as similar as Y(III) vs. Ho(III). Apparently, the change in the local environment between the surfaces affects the two twin elements differently and, thus, shifts the small gap in halide affinities between the two. Comparable experimental and computational studies of Y(III) and Ho(III) affinities in solutions containing both HF and HCl could give more insight into these subtle differences and would be the next step to elucidate the composition in fluoride-rich ores originating from hydrothermal veins.

4. Conclusions

The adsorptions of HF, HCl, and H₂O onto the four most abundant surfaces of YF₃ and HoF₃ were studied by applying periodic density functional theory. Comparing the two halides, we found that both MF₃ bind HF notably stronger than HCl for all three stoichiometric surfaces. We found that the adsorption energy of H₂O is insensitive to the surface cut. Due to this surface insensitivity, the slight preference for HoF₃ over YF₃ remains constant. On the contrary, the adsorption energies of HF and HCl are sensitive to the surface. For the latter, this also shows within the partial charges. For the rather bulk-like surface of (010) with low metal accessibility, the preference for HoF₃ is comparable to that shown by H₂O. The adsorptions of HF and HCl onto stoichiometric surfaces with more accessible M${}_{\mathrm{surf}}$ are considerably stronger, showing the strongest H-bonds and, thus, the largest structural changes upon adsorption. These also show varying metal affinities. HF and HCl both show the strongest preference for HoF₃ over YF₃ within (100), a surface that is also much more abundant in the heavier twin trifluoride. On the other hand, (011) prefers YF₃. Finally, the largest preference for YF₃ is found for the hydride-forming adsorptions onto the F-substoichiometric (101).